Fooled by intuition

I have heard too many times in various financial math classes that one of the goals were to “develop intuition” about some concept. More often than not it turned out to be just a poor excuse for not going into technical details. I hope the reason for that was the low expectation of the audience’s intellectual capabilities rather than the lecturer’s sloppy preparation. The proper course of events would be, naturally, to get the students to firmly grasp the subject in the finest detail being as technical as possible and achieve lucid understanding. Tons of homework and discussions would help here. Then the intuition would grow by itself just by virtue of the concept’s being now a natural component of a student’s “cloud of knowledge”. All that is not practical of course if there is no foundation to build upon. In such a case the lame “we need to develop intuition first” is the only way to mark a topic as “covered”.

The recent article by Dan Goldstein and Nassim Taleb “We don’t quite know what we are talking about when we talk about volatility.” presents an example of glaring incompetence among portfolio managers, quantitative analysts and students of graduate programs in financial engineering i.e. people who are supposed to know a thing or two about volatility. It turned out that when asked for quick answer they did not really see a difference betwean absolute mean deviation and sample standard deviation. So much for the advanced degrees and important looks. Not surprisingly all of them could write the obvious formulas correctly, it was the intuition that fooled them.

“Those who cannot remember the past…

…are condemned to repeat it.” (George Santayana.) I doubt there exist many people capable of rediscovering stochastic calculus but it is surprising how many “financial mathematicians” claim to know it while demonstrating utter ignorance of the foundations. The 2004 paper “A short history of stochastic integration and mathematical finance the early years, 1880–1970″ by Protter and Jarrow documents the history of mathematical finance in great detail. I am convinced that knowing the events leading to discoveries of certain difficult to understand mathematical facts makes the facts themselves much more natural and accessible. If you have ever been puzzled by, say, Itō isometry or Doob-Meyer decomposition, the paper will show all the gradual refinements the ideas underwent. There are also also all kinds of less mathematical stories in the text – like how American and European options got their names.

In conclusion, here is another, less famous, part of the quote above: “…when experience is not retained, …, infancy is perpetual.”

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